Question Number 217300 by peter frank last updated on 09/Mar/25 Answered by Marzuk last updated on 09/Mar/25 $$\:\:\:\:\:\:\:\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }\:−\:\mathrm{2}{a}\frac{{dy}}{{dx}}\:+\:\left({a}^{\mathrm{2}} \:+\:{b}^{\mathrm{2}} \right){y}\:=\:\mathrm{0} \\ $$$${or},\frac{{dy}'}{{dx}}\:−\:\mathrm{2}{a}\frac{{d}}{{dx}}\:\left[{e}^{{ax}} {sin}\left({bx}\right)\:\right]\:+\:{a}^{\mathrm{2}}…
Question Number 217314 by Tawa11 last updated on 09/Mar/25 $$\mathrm{How}\:\mathrm{is}\:\:\:\psi^{\mathrm{2}} \left(\mathrm{1}\right)\:\:=\:\:−\:\:\mathrm{2}\zeta\left(\mathrm{3}\right) \\ $$$$\:\:\:\:\:\:\mathrm{and}\:\:\:\:\psi^{\mathrm{2}} \left(\frac{\mathrm{1}}{\mathrm{2}}\right)\:\:\:=\:\:\:−\:\:\mathrm{14}\zeta\left(\mathrm{3}\right)\:\:\:\:\:\:\:??? \\ $$ Commented by mr W last updated on 10/Mar/25 $${with}\:\psi^{\mathrm{2}}…
Question Number 217299 by peter frank last updated on 09/Mar/25 Answered by mr W last updated on 10/Mar/25 $${x}={r}\:\mathrm{cos}\:\theta \\ $$$${y}={r}\:\mathrm{sin}\:\theta \\ $$$$\left({r}\:\mathrm{cos}\:\theta−\mathrm{1}\right)^{\mathrm{2}} +\left({r}\:\mathrm{sin}\:\theta\right)^{\mathrm{2}} =\mathrm{16}…
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Question Number 217289 by Frix last updated on 08/Mar/25 $$\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\mathrm{sin}^{−\mathrm{1}} \:\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}+{x}−{x}^{\mathrm{2}} }}\:{dx}=? \\ $$ Commented by Ghisom last updated on 11/Mar/25 $$\mathrm{we}\:\mathrm{can}\:\mathrm{use}\:\mathrm{partial}\:\mathrm{integration} \\…
Question Number 217290 by mnjuly1970 last updated on 08/Mar/25 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\mathrm{ln}^{\mathrm{2}} \left(\mathrm{1}−{x}\right)}{{x}^{\mathrm{2}} }\:{dx}=\:? \\ $$$$ \\ $$$$ \\ $$ Answered by profcedricjunior…
Question Number 217291 by ArshadS last updated on 08/Mar/25 $$\mathrm{Solve}: \\ $$$$\frac{{x}+\mathrm{2}}{{x}−\mathrm{3}}−\frac{{x}−\mathrm{1}}{{x}+\mathrm{4}}=\frac{\mathrm{10}}{{x}^{\mathrm{2}} +{x}−\mathrm{12}} \\ $$ Answered by Hanuda354 last updated on 08/Mar/25 $$\frac{\left({x}^{\mathrm{2}} +\mathrm{6}{x}+\mathrm{8}\right)−\left({x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{3}\right)}{{x}^{\mathrm{2}}…
Question Number 217244 by ArshadS last updated on 07/Mar/25 $$\:\mathrm{Find}\:\mathrm{all}\:\mathrm{two}-\mathrm{digit}\:\mathrm{numbers}\:\mathrm{such}\:\mathrm{that} \\ $$$$\mathrm{when}\:\mathrm{the}\:\mathrm{number}\:\mathrm{is}\:\mathrm{divided}\:\mathrm{by} \\ $$$$\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{its}\:\mathrm{digits}\:\mathrm{the}\:\mathrm{quotient}\: \\ $$$$\mathrm{is}\:\mathrm{4}\:\mathrm{and}\:\mathrm{the}\:\mathrm{remainder}\:\mathrm{is}\:\mathrm{3}. \\ $$ Answered by Frix last updated on 07/Mar/25…
Question Number 217245 by OmoloyeMichael last updated on 07/Mar/25 $${find}\:{the}\:{following}\:{differential}\:{equation}\: \\ $$$${by}\:{eliminating}\:{the}\:{arbritrary}\:{constant} \\ $$$$\left(\mathrm{1}\right){y}={Ae}^{{x}} +{Bcosx} \\ $$$$\left(\mathrm{2}\right)\:{xy}={Ae}^{{x}} +{Be}^{−{x}} +{x}^{\mathrm{2}} \\ $$$$ \\ $$ Answered by…
Question Number 217262 by ArshadS last updated on 07/Mar/25 $${Solve}: \\ $$$$\frac{{x}^{\mathrm{2}} +\mathrm{3}{x}}{{x}^{\mathrm{3}} −\mathrm{4}{x}}−\frac{\mathrm{2}}{{x}^{\mathrm{2}} +\mathrm{2}{x}}=\frac{\mathrm{1}}{{x}−\mathrm{2}} \\ $$ Answered by ibrahimmatematic last updated on 07/Mar/25 $$\frac{{x}\left({x}+\mathrm{3}\right)}{{x}\left({x}−\mathrm{2}\right)\left({x}+\mathrm{2}\right)}−\frac{\mathrm{2}}{{x}\left({x}+\mathrm{2}\right)}=\frac{\mathrm{1}}{{x}−\mathrm{2}}…